<environment: R_GlobalEnv>
In practice, very few samples return MGIT time-to-positivity values between 30 and 42 days. While this range may be important for individual diagnostic purposes, the TTP values captured in this range may not contribute meaningfully to understanding the relative TTP trajectories at the regimen-level. We investigate whether using a lower limit of detection for longitudinal time-to-positivity modeling will improve precision for detecting differences between treatments, resulting in shorter trial times and improved power for performing regimen selection.
Our objective is to examine existing TTP data from various case studies to better define the trajectory and variance of regimen-level TTP over time, while examining the impact of alternate limits of detection on power.
REMoxTB
PanACEA MAMS-TB
We will restrict to only those with:
result = 0,1,2 (i.e., only those with a Negative (0), Positive (1), or Unconfirmed Positive (2) result)bact = 1 (i.e., MGIT)weeks <= 8 (i.e., only looking at observations within 8 weeks of randomization)!box_mitt %in% c(10,20,30) excluding those with late screening failuresWe restrict to those with:
WEEK <= 8 (i.e., only looking at observations within 8 weeks of randomization)
!is.na(DV) (i.e., only those with an observed time to positivity)
<environment: R_GlobalEnv>
Models: Bayesian (linear fit), Burger bi-linear model, etc.
LOQ: 25, 30, 42
| ttp | n | prop |
|---|---|---|
| [0,30) | 11058 | 0.7505 |
| [30,42) | 221 | 0.0150 |
| [42,45) | 3455 | 0.2345 |
| ttp | n | prop |
|---|---|---|
| [0,30) | 2265 | 0.7325 |
| [30,42) | 117 | 0.0378 |
| [42,45) | 710 | 0.2296 |
| week | ttp | n | prop |
|---|---|---|---|
| 0 | [0,30) | 3291 | 0.9213 |
| 0 | [30,42) | 5 | 0.0014 |
| 0 | [42,45) | 276 | 0.0773 |
| 1 | [0,30) | 1434 | 0.8792 |
| 1 | [30,42) | 5 | 0.0031 |
| 1 | [42,45) | 192 | 0.1177 |
| 2 | [0,30) | 1327 | 0.8656 |
| 2 | [30,42) | 13 | 0.0085 |
| 2 | [42,45) | 193 | 0.1259 |
| 3 | [0,30) | 1237 | 0.8313 |
| 3 | [30,42) | 13 | 0.0087 |
| 3 | [42,45) | 238 | 0.1599 |
| 4 | [0,30) | 1086 | 0.7521 |
| 4 | [30,42) | 29 | 0.0201 |
| 4 | [42,45) | 329 | 0.2278 |
| 5 | [0,30) | 939 | 0.6726 |
| 5 | [30,42) | 29 | 0.0208 |
| 5 | [42,45) | 428 | 0.3066 |
| 6 | [0,30) | 792 | 0.5781 |
| 6 | [30,42) | 47 | 0.0343 |
| 6 | [42,45) | 531 | 0.3876 |
| 7 | [0,30) | 621 | 0.4510 |
| 7 | [30,42) | 52 | 0.0378 |
| 7 | [42,45) | 704 | 0.5113 |
| 8 | [0,30) | 331 | 0.3586 |
| 8 | [30,42) | 28 | 0.0303 |
| 8 | [42,45) | 564 | 0.6111 |
| week | ttp | n | prop |
|---|---|---|---|
| 0 | [0,30) | 394 | 0.9975 |
| 0 | [30,42) | 1 | 0.0025 |
| 1 | [0,30) | 387 | 0.9724 |
| 1 | [30,42) | 2 | 0.0050 |
| 1 | [42,45) | 9 | 0.0226 |
| 2 | [0,30) | 344 | 0.9198 |
| 2 | [30,42) | 4 | 0.0107 |
| 2 | [42,45) | 26 | 0.0695 |
| 3 | [0,30) | 314 | 0.9075 |
| 3 | [30,42) | 6 | 0.0173 |
| 3 | [42,45) | 26 | 0.0751 |
| 4 | [0,30) | 252 | 0.7522 |
| 4 | [30,42) | 17 | 0.0507 |
| 4 | [42,45) | 66 | 0.1970 |
| 5 | [0,30) | 209 | 0.6276 |
| 5 | [30,42) | 29 | 0.0871 |
| 5 | [42,45) | 95 | 0.2853 |
| 6 | [0,30) | 164 | 0.5325 |
| 6 | [30,42) | 17 | 0.0552 |
| 6 | [42,45) | 127 | 0.4123 |
| 7 | [0,30) | 112 | 0.3836 |
| 7 | [30,42) | 22 | 0.0753 |
| 7 | [42,45) | 158 | 0.5411 |
| 8 | [0,30) | 89 | 0.2862 |
| 8 | [30,42) | 19 | 0.0611 |
| 8 | [42,45) | 203 | 0.6527 |
Observed TTP trajectories, where anything at or above 42 receives a value of 42.
Panel A
Panel B
Observed TTP trajectories, where anything at or above 42 receives a value of 42.
Panel A
Panel B
[WANT ALLUVIAL PLOT… ]
Distribution of TTP measures at each week post-randomization.
Idea: Maybe this should a “relative” to 42 plot, rather than an absolute plot? Would that make it easier to read? or add in limited horizontal lines?
| week | 25 days | 30 days | 35 days | 42 days | Difference in proportions: 42 v 30 days |
|---|---|---|---|---|---|
| 0 | 0.9197 | 0.9213 | 0.9225 | 0.9227 | 0.0014 |
| 1 | 0.8743 | 0.8792 | 0.8792 | 0.8823 | 0.0031 |
| 2 | 0.8565 | 0.8656 | 0.8689 | 0.8741 | 0.0085 |
| 3 | 0.8132 | 0.8313 | 0.8367 | 0.8401 | 0.0087 |
| 4 | 0.7216 | 0.7521 | 0.7632 | 0.7722 | 0.0201 |
| 5 | 0.6426 | 0.6726 | 0.6862 | 0.6934 | 0.0208 |
| 6 | 0.5350 | 0.5781 | 0.5978 | 0.6124 | 0.0343 |
| 7 | 0.4110 | 0.4510 | 0.4742 | 0.4887 | 0.0378 |
| 8 | 0.3109 | 0.3586 | 0.3749 | 0.3889 | 0.0303 |
| week | 25 days | 30 days | 35 days | 42 days | Difference in proportions: 42 v 30 days |
|---|---|---|---|---|---|
| 0 | 0.9975 | 0.9975 | 0.9975 | 1.0000 | 0.0025 |
| 1 | 0.9623 | 0.9724 | 0.9749 | 0.9774 | 0.0050 |
| 2 | 0.9011 | 0.9198 | 0.9305 | 0.9305 | 0.0107 |
| 3 | 0.8815 | 0.9075 | 0.9162 | 0.9249 | 0.0173 |
| 4 | 0.7045 | 0.7522 | 0.7940 | 0.8030 | 0.0507 |
| 5 | 0.5856 | 0.6276 | 0.6607 | 0.7147 | 0.0871 |
| 6 | 0.4610 | 0.5325 | 0.5519 | 0.5877 | 0.0552 |
| 7 | 0.3288 | 0.3836 | 0.4315 | 0.4589 | 0.0753 |
| 8 | 0.2444 | 0.2862 | 0.3087 | 0.3473 | 0.0611 |
| Estimate | CI.l | CI.u | CI width | Point Estimation | CI Estimation | |
|---|---|---|---|---|---|---|
| LOQ = 42 | ||||||
| HR20ZM.weeks | 0.138 | 0.124 | 0.154 | 0.030 | mode | hdi |
| HR20ZQ.weeks | 0.121 | 0.104 | 0.137 | 0.033 | mode | hdi |
| HR35ZE.weeks | 0.144 | 0.126 | 0.160 | 0.034 | mode | hdi |
| HRZE.weeks | 0.128 | 0.116 | 0.138 | 0.022 | mode | hdi |
| HRZQ.weeks | 0.122 | 0.104 | 0.137 | 0.033 | mode | hdi |
| LOQ = 30 | ||||||
| HR20ZM.weeks | 0.132 | 0.117 | 0.146 | 0.029 | mode | hdi |
| HR20ZQ.weeks | 0.116 | 0.101 | 0.130 | 0.029 | mode | hdi |
| HR35ZE.weeks | 0.138 | 0.123 | 0.155 | 0.032 | mode | hdi |
| HRZE.weeks | 0.122 | 0.109 | 0.131 | 0.022 | mode | hdi |
| HRZQ.weeks | 0.115 | 0.098 | 0.129 | 0.031 | mode | hdi |
| LOQ = 25 | ||||||
| HR20ZM.weeks | 0.127 | 0.114 | 0.142 | 0.028 | mode | hdi |
| HR20ZQ.weeks | 0.117 | 0.099 | 0.129 | 0.030 | mode | hdi |
| HR35ZE.weeks | 0.137 | 0.121 | 0.155 | 0.034 | mode | hdi |
| HRZE.weeks | 0.120 | 0.109 | 0.131 | 0.022 | mode | hdi |
| HRZQ.weeks | 0.115 | 0.097 | 0.128 | 0.031 | mode | hdi |
| Estimate | CI.l | CI.u | CI width | Point Estimation | CI Estimation | |
|---|---|---|---|---|---|---|
| LOQ = 42 | ||||||
| 1. 2EHRZ/4HR.weeks | 0.095 | 0.090 | 0.100 | 0.010 | mode | hdi |
| 2. 2MHRZ/2MHR.weeks | 0.104 | 0.100 | 0.109 | 0.009 | mode | hdi |
| 3. 2EMRZ/2MR.weeks | 0.107 | 0.102 | 0.111 | 0.009 | mode | hdi |
| LOQ = 30 | ||||||
| 1. 2EHRZ/4HR.weeks | 0.089 | 0.085 | 0.093 | 0.008 | mode | hdi |
| 2. 2MHRZ/2MHR.weeks | 0.097 | 0.094 | 0.102 | 0.008 | mode | hdi |
| 3. 2EMRZ/2MR.weeks | 0.099 | 0.095 | 0.103 | 0.008 | mode | hdi |
| LOQ = 25 | ||||||
| 1. 2EHRZ/4HR.weeks | 0.086 | 0.082 | 0.090 | 0.008 | mode | hdi |
| 2. 2MHRZ/2MHR.weeks | 0.095 | 0.091 | 0.099 | 0.008 | mode | hdi |
| 3. 2EMRZ/2MR.weeks | 0.097 | 0.093 | 0.100 | 0.007 | mode | hdi |
| key | point.estimate.ratio.30.42 | CI.width.ratio.30.42 | point.estimate.ratio.25.42 | CI.width.ratio.25.42 |
|---|---|---|---|---|
| HR20ZM.weeks | 0.9565 | 0.9667 | 0.9203 | 0.9333 |
| HR20ZQ.weeks | 0.9587 | 0.8788 | 0.9669 | 0.9091 |
| HR35ZE.weeks | 0.9583 | 0.9412 | 0.9514 | 1.0000 |
| HRZE.weeks | 0.9531 | 1.0000 | 0.9375 | 1.0000 |
| HRZQ.weeks | 0.9426 | 0.9394 | 0.9426 | 0.9394 |
| key | point.estimate.ratio | CI.width.ratio |
|---|---|---|
| 1. 2EHRZ/4HR.weeks | 0.9368 | 0.8000 |
| 2. 2MHRZ/2MHR.weeks | 0.9327 | 0.8889 |
| 3. 2EMRZ/2MR.weeks | 0.9252 | 0.8889 |
| regimen | coefficient | Estimate | CI.l | CI.u | CI width | Point Estimation | CI Estimation | LOQ |
|---|---|---|---|---|---|---|---|---|
| beta_1 | ||||||||
| HR20ZM | beta1 | 0.000 | -1.559 | 0.221 | 1.780 | mode | qi | 42 |
| HR20ZM | beta1 | -0.825 | -0.829 | 0.272 | 1.101 | mode | qi | 30 |
| HR20ZQ | beta1 | 0.125 | -0.821 | 0.216 | 1.037 | mode | qi | 42 |
| HR20ZQ | beta1 | -0.821 | -0.825 | 0.264 | 1.089 | mode | qi | 30 |
| HR35ZE | beta1 | 0.689 | -0.763 | 0.689 | 1.452 | mode | qi | 42 |
| HR35ZE | beta1 | -0.788 | -0.790 | 0.276 | 1.066 | mode | qi | 30 |
| HRZE | beta1 | 0.118 | 0.116 | 1.253 | 1.137 | mode | qi | 42 |
| HRZE | beta1 | -0.797 | -0.800 | 0.275 | 1.075 | mode | qi | 30 |
| HRZQ | beta1 | 0.121 | 0.122 | 1.350 | 1.228 | mode | qi | 42 |
| HRZQ | beta1 | -0.809 | -0.813 | 0.265 | 1.078 | mode | qi | 30 |
| beta_2 | ||||||||
| HR20ZM | beta2 | -0.146 | -1.707 | -0.052 | 1.655 | mode | qi | 42 |
| HR20ZM | beta2 | -0.973 | -0.976 | -0.032 | 0.944 | mode | qi | 30 |
| HR20ZQ | beta2 | -0.208 | -0.937 | -0.053 | 0.884 | mode | qi | 42 |
| HR20ZQ | beta2 | -0.933 | -0.938 | -0.077 | 0.861 | mode | qi | 30 |
| HR35ZE | beta2 | 0.519 | -0.913 | 0.518 | 1.431 | mode | qi | 42 |
| HR35ZE | beta2 | -0.933 | -0.936 | -0.054 | 0.882 | mode | qi | 30 |
| HRZE | beta2 | 1.136 | -0.478 | 1.136 | 1.614 | mode | qi | 42 |
| HRZE | beta2 | -0.927 | -0.928 | -0.041 | 0.887 | mode | qi | 30 |
| HRZQ | beta2 | -0.212 | -0.208 | 1.240 | 1.448 | mode | qi | 42 |
| HRZQ | beta2 | -0.927 | -0.929 | -0.058 | 0.871 | mode | qi | 30 |
| regimen | coefficient | Estimate | CI.l | CI.u | CI width | Point Estimation | CI Estimation | LOQ |
|---|---|---|---|---|---|---|---|---|
| beta_1 | ||||||||
| 2EHRZ/4HR | beta1 | 0.098 | 0.090 | 0.219 | 0.129 | mode | qi | 42 |
| 2EHRZ/4HR | beta1 | 0.092 | 0.017 | 0.233 | 0.216 | mode | qi | 30 |
| 2EMRZ/2MR | beta1 | 0.098 | 0.096 | 0.225 | 0.129 | mode | qi | 42 |
| 2EMRZ/2MR | beta1 | 0.098 | 0.010 | 0.236 | 0.226 | mode | qi | 30 |
| 2MHRZ/2MHR | beta1 | 0.106 | 0.097 | 0.219 | 0.122 | mode | qi | 42 |
| 2MHRZ/2MHR | beta1 | 0.093 | 0.050 | 0.229 | 0.179 | mode | qi | 30 |
| beta_2 | ||||||||
| 2EHRZ/4HR | beta2 | -0.140 | -0.370 | -0.088 | 0.282 | mode | qi | 42 |
| 2EHRZ/4HR | beta2 | -0.129 | -1.346 | -0.084 | 1.262 | mode | qi | 30 |
| 2EMRZ/2MR | beta2 | -0.128 | -0.365 | -0.097 | 0.268 | mode | qi | 42 |
| 2EMRZ/2MR | beta2 | -0.109 | -1.281 | -0.088 | 1.193 | mode | qi | 30 |
| 2MHRZ/2MHR | beta2 | -0.126 | -0.374 | -0.098 | 0.276 | mode | qi | 42 |
| 2MHRZ/2MHR | beta2 | -0.113 | -1.401 | -0.096 | 1.305 | mode | qi | 30 |
For the REMoxTB and MAMS-TB data, point estimates in the 30-day models decrease relative to the 42-day models, as expected when “removing” data at the upper end of the spectrum.
However, credible intervals (e.g., precision) remain either the same or improve in the 30-day models relative to the 42-day models. In the REMoxTB data, the CIs improve more than the point estimates shrink. This is also true for 3 out of 5 arms in the MAMS-TB data.
We’re not just interested in the estimation of TTP slopes. More importantly, we want to directly address whether improved estimation allows us to make “better” decisions, ideally earlier. Therefore, this section will look at the ability to differentiate “promising” regimens relative to control, where promising is assumed to mean those with steeper changes in log10(TTP) than control regimens.
# A tibble: 3 × 2
which.LOQ.best `n()`
<chr> <int>
1 25 days 24
2 30 days 27
3 42 days 9
# A tibble: 3 × 2
which.LOQ.best `n()`
<chr> <int>
1 25 days 3
2 30 days 3
3 42 days 6
For the MAMS-TB data, using a 30-day limit of quantification improves the ability to differentiate regimens relative to the control. The estimated posterior probability (e.g., “confidence”) that a given regimen’s rate of change is as steep or steeper than then the control regimen’s rate of change is best for nearly all regimens with a 30- rather than 42-day limit of quantification.
The same trend as was observed in MAMS is not observed in the REMoxTB data, which is perplexing. The 42-day limit of quantification is observed to correlate with a stronger posterior probability of differentiation between the novel regimens and the control (HRZE).
Should we be doing more of a grid-search or can we motivate this better with a S-N exploration first?
Not super satisfied with this plot, but I do like that it seems to confirm that the deviance in replicates increases as the expected value of TTP increases (e.g., with time).
| Estimate | CI.l | CI.u | CI width | Point Estimation | CI Estimation | |
|---|---|---|---|---|---|---|
| LOQ = 42 | ||||||
| HR20ZM.weeks | 0.118 | 0.105 | 0.136 | 0.031 | mode | hdi |
| HR20ZQ.weeks | 0.109 | 0.089 | 0.121 | 0.032 | mode | hdi |
| HR35ZE.weeks | 0.124 | 0.108 | 0.142 | 0.034 | mode | hdi |
| HRZE.weeks | 0.113 | 0.101 | 0.126 | 0.025 | mode | hdi |
| HRZQ.weeks | 0.110 | 0.091 | 0.124 | 0.033 | mode | hdi |
| LOQ = 30 | ||||||
| HR20ZM.weeks | 0.110 | 0.096 | 0.125 | 0.029 | mode | hdi |
| HR20ZQ.weeks | 0.101 | 0.083 | 0.114 | 0.031 | mode | hdi |
| HR35ZE.weeks | 0.117 | 0.100 | 0.134 | 0.034 | mode | hdi |
| HRZE.weeks | 0.105 | 0.093 | 0.116 | 0.023 | mode | hdi |
| HRZQ.weeks | 0.102 | 0.084 | 0.114 | 0.030 | mode | hdi |
| LOQ = 25 | ||||||
| HR20ZM.weeks | 0.104 | 0.091 | 0.119 | 0.028 | mode | hdi |
| HR20ZQ.weeks | 0.097 | 0.080 | 0.110 | 0.030 | mode | hdi |
| HR35ZE.weeks | 0.111 | 0.097 | 0.129 | 0.032 | mode | hdi |
| HRZE.weeks | 0.102 | 0.090 | 0.113 | 0.023 | mode | hdi |
| HRZQ.weeks | 0.098 | 0.081 | 0.110 | 0.029 | mode | hdi |
| Estimate | CI.l | CI.u | CI width | Point Estimation | CI Estimation | |
|---|---|---|---|---|---|---|
| LOQ = 42 | ||||||
| 1. 2EHRZ/4HR.weeks | 0.079 | 0.073 | 0.084 | 0.011 | mode | hdi |
| 2. 2MHRZ/2MHR.weeks | 0.083 | 0.079 | 0.088 | 0.009 | mode | hdi |
| 3. 2EMRZ/2MR.weeks | 0.087 | 0.081 | 0.092 | 0.011 | mode | hdi |
| LOQ = 30 | ||||||
| 1. 2EHRZ/4HR.weeks | 0.070 | 0.065 | 0.075 | 0.010 | mode | hdi |
| 2. 2MHRZ/2MHR.weeks | 0.074 | 0.069 | 0.077 | 0.008 | mode | hdi |
| 3. 2EMRZ/2MR.weeks | 0.076 | 0.072 | 0.081 | 0.009 | mode | hdi |
| LOQ = 25 | ||||||
| 1. 2EHRZ/4HR.weeks | 0.065 | 0.061 | 0.070 | 0.009 | mode | hdi |
| 2. 2MHRZ/2MHR.weeks | 0.069 | 0.065 | 0.073 | 0.008 | mode | hdi |
| 3. 2EMRZ/2MR.weeks | 0.072 | 0.067 | 0.076 | 0.009 | mode | hdi |
Family: gaussian
Links: mu = identity; sigma = identity
Formula: log10(dtp_25) | cens(censored_25) ~ weeks + (1 + weeks | patient.id + Treatm_arm)
Data: df_analysis_mams (Number of observations: 3092)
Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup draws = 4000
Group-Level Effects:
~patient.id (Number of levels: 363)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
sd(Intercept) 0.11 0.01 0.09 0.14 1.00 1150
sd(weeks) 0.04 0.00 0.04 0.05 1.01 684
cor(Intercept,weeks) 0.07 0.16 -0.20 0.45 1.01 362
Tail_ESS
sd(Intercept) 1993
sd(weeks) 1471
cor(Intercept,weeks) 677
~Treatm_arm (Number of levels: 5)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
sd(Intercept) 0.02 0.03 0.00 0.08 1.00 1648
sd(weeks) 0.02 0.02 0.00 0.06 1.00 776
cor(Intercept,weeks) -0.17 0.58 -0.98 0.92 1.00 1488
Tail_ESS
sd(Intercept) 2290
sd(weeks) 896
cor(Intercept,weeks) 2707
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 0.76 0.02 0.73 0.80 1.00 2955 2264
weeks 0.12 0.01 0.10 0.15 1.00 1100 751
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.26 0.00 0.25 0.27 1.00 2543 2291
Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
Family: gaussian
Links: mu = identity; sigma = identity
Formula: log10(dtp_30) | cens(censored_30) ~ weeks + (1 + weeks | patient.id + Treatm_arm)
Data: df_analysis_mams (Number of observations: 3092)
Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup draws = 4000
Group-Level Effects:
~patient.id (Number of levels: 363)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
sd(Intercept) 0.12 0.01 0.09 0.14 1.01 905
sd(weeks) 0.05 0.00 0.04 0.05 1.02 405
cor(Intercept,weeks) 0.09 0.17 -0.21 0.46 1.03 208
Tail_ESS
sd(Intercept) 1463
sd(weeks) 1002
cor(Intercept,weeks) 372
~Treatm_arm (Number of levels: 5)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
sd(Intercept) 0.02 0.02 0.00 0.08 1.00 1881
sd(weeks) 0.02 0.02 0.00 0.06 1.01 676
cor(Intercept,weeks) -0.15 0.58 -0.97 0.93 1.00 1024
Tail_ESS
sd(Intercept) 2511
sd(weeks) 748
cor(Intercept,weeks) 1858
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 0.76 0.02 0.73 0.80 1.00 3045 2321
weeks 0.12 0.01 0.10 0.15 1.00 1433 1001
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.26 0.00 0.26 0.27 1.00 2984 2722
Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
Family: gaussian
Links: mu = identity; sigma = identity
Formula: log10(dtp_42) | cens(censored_42) ~ weeks + (1 + weeks | patient.id + Treatm_arm)
Data: df_analysis_mams (Number of observations: 3092)
Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup draws = 4000
Group-Level Effects:
~patient.id (Number of levels: 363)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
sd(Intercept) 0.13 0.01 0.10 0.15 1.00 1284
sd(weeks) 0.05 0.00 0.04 0.06 1.01 600
cor(Intercept,weeks) -0.01 0.14 -0.24 0.29 1.01 304
Tail_ESS
sd(Intercept) 1779
sd(weeks) 1229
cor(Intercept,weeks) 622
~Treatm_arm (Number of levels: 5)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
sd(Intercept) 0.02 0.03 0.00 0.09 1.00 1959
sd(weeks) 0.02 0.02 0.00 0.06 1.01 756
cor(Intercept,weeks) -0.13 0.59 -0.97 0.93 1.00 1352
Tail_ESS
sd(Intercept) 2465
sd(weeks) 1230
cor(Intercept,weeks) 2346
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 0.76 0.02 0.72 0.80 1.00 3390 2943
weeks 0.13 0.01 0.11 0.16 1.00 1528 1009
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.28 0.00 0.27 0.28 1.00 3169 2511
Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
Family: gaussian
Links: mu = identity; sigma = identity
Formula: log10(dtp_30) | cens(censored_30) ~ alpha + beta1 * weeks + beta2 * gamma * log((exp((weeks - kappa)/gamma) + exp(-(weeks - kappa)/gamma))/(exp(kappa/gamma) + exp(-kappa/gamma)))
alpha ~ 1 + (1 | patient.id + Treatm_arm)
beta1 ~ 1 + (1 | patient.id + Treatm_arm)
beta2 ~ 1 + (1 | patient.id + Treatm_arm)
kappa ~ 1 + (1 | patient.id + Treatm_arm)
gamma ~ 1 + (1 | patient.id + Treatm_arm)
Data: filter(df_analysis_mams, DV != -99) (Number of observations: 3092)
Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup draws = 4000
Group-Level Effects:
~patient.id (Number of levels: 363)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(alpha_Intercept) 0.14 0.01 0.12 0.16 1.80 17 84
sd(beta1_Intercept) 0.03 0.01 0.00 0.04 2.99 5 13
sd(beta2_Intercept) 0.04 0.01 0.03 0.05 1.70 6 33
sd(kappa_Intercept) 0.53 0.42 0.06 1.22 2.18 6 11
sd(gamma_Intercept) 0.14 0.14 0.00 0.48 2.64 6 13
~Treatm_arm (Number of levels: 5)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(alpha_Intercept) 0.03 0.02 0.00 0.07 1.33 14 39
sd(beta1_Intercept) 0.01 0.01 0.00 0.05 1.21 20 92
sd(beta2_Intercept) 0.02 0.02 0.00 0.10 1.91 6 12
sd(kappa_Intercept) 1.64 0.61 1.08 3.18 1.35 10 79
sd(gamma_Intercept) 0.19 0.22 0.01 0.80 1.59 13 67
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
alpha_Intercept 0.70 0.04 0.63 0.75 2.16 5 23
beta1_Intercept -0.05 0.43 -0.80 0.27 2.63 5 14
beta2_Intercept -0.31 0.36 -0.94 -0.04 2.88 5 13
kappa_Intercept 4.31 3.39 2.03 10.17 1.75 6 13
gamma_Intercept 0.57 0.35 0.15 1.36 1.61 7 12
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.25 0.00 0.24 0.26 1.30 11 56
Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
Family: gaussian
Links: mu = identity; sigma = identity
Formula: log10(dtp_42) | cens(censored_42) ~ alpha + beta1 * weeks + beta2 * gamma * log((exp((weeks - kappa)/gamma) + exp(-(weeks - kappa)/gamma))/(exp(kappa/gamma) + exp(-kappa/gamma)))
alpha ~ 1 + (1 | patient.id + Treatm_arm)
beta1 ~ 1 + (1 | patient.id + Treatm_arm)
beta2 ~ 1 + (1 | patient.id + Treatm_arm)
kappa ~ 1 + (1 | patient.id + Treatm_arm)
gamma ~ 1 + (1 | patient.id + Treatm_arm)
Data: df_analysis_mams (Number of observations: 3092)
Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup draws = 4000
Group-Level Effects:
~patient.id (Number of levels: 363)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(alpha_Intercept) 0.13 0.01 0.11 0.16 1.90 7 19
sd(beta1_Intercept) 0.04 0.01 0.03 0.05 2.41 5 23
sd(beta2_Intercept) 0.11 0.12 0.04 0.32 2.99 5 11
sd(kappa_Intercept) 0.97 0.81 0.09 2.97 2.74 5 12
sd(gamma_Intercept) 1.92 3.05 0.01 7.28 2.78 5 20
~Treatm_arm (Number of levels: 5)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(alpha_Intercept) 0.03 0.02 0.00 0.05 1.76 8 40
sd(beta1_Intercept) 0.51 0.63 0.00 2.32 2.04 5 17
sd(beta2_Intercept) 0.58 0.55 0.00 1.82 2.85 5 17
sd(kappa_Intercept) 0.99 0.71 0.14 2.56 1.97 6 13
sd(gamma_Intercept) 5.98 9.15 0.04 21.97 2.79 5 26
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
alpha_Intercept 0.71 0.04 0.66 0.77 2.00 6 21
beta1_Intercept 0.10 0.24 -0.59 0.33 2.23 6 36
beta2_Intercept -0.05 0.35 -0.71 0.50 3.01 5 13
kappa_Intercept 6.37 3.52 2.07 10.92 2.99 5 37
gamma_Intercept 1.13 0.44 0.29 1.76 2.25 5 31
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.27 0.01 0.26 0.27 1.64 7 40
Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
Family: gaussian
Links: mu = identity; sigma = identity
Formula: log10(dtp_30) | cens(censored_30) ~ weeks + (1 + weeks | trial_no + treat)
Data: df_analysis_remox (Number of observations: 14734)
Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
total post-warmup draws = 8000
Group-Level Effects:
~treat (Number of levels: 3)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
sd(Intercept) 0.04 0.09 0.00 0.26 1.00 1788
sd(weeks) 0.03 0.04 0.00 0.14 1.00 1550
cor(Intercept,weeks) 0.13 0.61 -0.95 0.98 1.00 3108
Tail_ESS
sd(Intercept) 1735
sd(weeks) 1331
cor(Intercept,weeks) 2857
~trial_no (Number of levels: 1821)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
sd(Intercept) 0.13 0.00 0.12 0.14 1.00 2587
sd(weeks) 0.04 0.00 0.04 0.04 1.01 756
cor(Intercept,weeks) -0.27 0.05 -0.35 -0.17 1.01 740
Tail_ESS
sd(Intercept) 4306
sd(weeks) 1659
cor(Intercept,weeks) 1947
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 0.87 0.05 0.79 0.93 1.00 2669 1896
weeks 0.10 0.02 0.05 0.14 1.00 1761 1336
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.23 0.00 0.23 0.24 1.00 4476 3652
Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
Family: gaussian
Links: mu = identity; sigma = identity
Formula: log10(dtp_42) | cens(censored_42) ~ weeks + (1 + weeks | trial_no + treat)
Data: df_analysis_remox (Number of observations: 14734)
Draws: 4 chains, each with iter = 4000; warmup = 2000; thin = 1;
total post-warmup draws = 8000
Group-Level Effects:
~treat (Number of levels: 3)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
sd(Intercept) 0.06 0.16 0.00 0.43 1.01 536
sd(weeks) 0.03 0.06 0.00 0.18 1.01 639
cor(Intercept,weeks) 0.14 0.61 -0.95 0.98 1.00 880
Tail_ESS
sd(Intercept) 361
sd(weeks) 769
cor(Intercept,weeks) 1711
~trial_no (Number of levels: 1821)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS
sd(Intercept) 0.13 0.01 0.13 0.14 1.01 404
sd(weeks) 0.04 0.00 0.04 0.05 1.03 214
cor(Intercept,weeks) -0.23 0.05 -0.32 -0.13 1.04 100
Tail_ESS
sd(Intercept) 1667
sd(weeks) 735
cor(Intercept,weeks) 175
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
Intercept 0.87 0.08 0.77 1.01 1.02 314 254
weeks 0.10 0.03 0.06 0.16 1.00 574 508
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.25 0.00 0.25 0.26 1.01 974 1751
Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
Family: gaussian
Links: mu = identity; sigma = identity
Formula: log10(dtp_30) | cens(censored_30) ~ alpha + beta1 * weeks + beta2 * gamma * log((exp((weeks - kappa)/gamma) + exp(-(weeks - kappa)/gamma))/(exp(kappa/gamma) + exp(-kappa/gamma)))
alpha ~ 1 + (1 | trial_no + treat)
beta1 ~ 1 + (1 | trial_no + treat)
beta2 ~ 1 + (1 | trial_no + treat)
kappa ~ 1 + (1 | trial_no + treat)
gamma ~ 1 + (1 | trial_no + treat)
Data: df_analysis_remox (Number of observations: 14734)
Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup draws = 4000
Group-Level Effects:
~treat (Number of levels: 3)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(alpha_Intercept) 0.02 0.01 0.00 0.06 1.47 8 22
sd(beta1_Intercept) 0.51 0.85 0.00 2.36 2.83 5 13
sd(beta2_Intercept) 0.48 0.50 0.00 1.84 2.75 5 16
sd(kappa_Intercept) 2.03 2.20 0.17 7.76 2.65 5 13
sd(gamma_Intercept) 21.73 18.17 0.03 63.99 3.12 5 11
~trial_no (Number of levels: 1821)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(alpha_Intercept) 0.12 0.00 0.11 0.12 1.31 11 32
sd(beta1_Intercept) 0.03 0.00 0.02 0.03 2.92 5 30
sd(beta2_Intercept) 0.22 0.15 0.01 0.51 1.86 6 16
sd(kappa_Intercept) 0.69 0.44 0.07 1.43 3.93 4 11
sd(gamma_Intercept) 4.71 5.31 0.01 15.57 2.81 5 27
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
alpha_Intercept 0.83 0.02 0.79 0.85 2.38 5 31
beta1_Intercept 0.55 0.76 0.07 2.09 2.36 5 12
beta2_Intercept -0.24 0.35 -1.05 0.42 2.00 5 11
kappa_Intercept 5.00 3.00 2.10 10.51 2.49 5 11
gamma_Intercept 1.09 0.56 0.17 1.91 2.06 5 48
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.23 0.00 0.22 0.23 2.54 5 15
Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).
Family: gaussian
Links: mu = identity; sigma = identity
Formula: log10(dtp_42) | cens(censored_42) ~ alpha + beta1 * weeks + beta2 * gamma * log((exp((weeks - kappa)/gamma) + exp(-(weeks - kappa)/gamma))/(exp(kappa/gamma) + exp(-kappa/gamma)))
alpha ~ 1 + (1 | trial_no + treat)
beta1 ~ 1 + (1 | trial_no + treat)
beta2 ~ 1 + (1 | trial_no + treat)
kappa ~ 1 + (1 | trial_no + treat)
gamma ~ 1 + (1 | trial_no + treat)
Data: df_analysis_remox (Number of observations: 14734)
Draws: 4 chains, each with iter = 2000; warmup = 1000; thin = 1;
total post-warmup draws = 4000
Group-Level Effects:
~treat (Number of levels: 3)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(alpha_Intercept) 0.03 0.11 0.00 0.28 1.33 10 48
sd(beta1_Intercept) 0.01 0.04 0.00 0.04 1.39 9 20
sd(beta2_Intercept) 0.27 0.48 0.00 1.81 2.60 5 27
sd(kappa_Intercept) 0.98 1.21 0.07 3.92 2.71 5 23
sd(gamma_Intercept) 14.39 10.41 0.04 38.32 2.61 5 12
~trial_no (Number of levels: 1821)
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sd(alpha_Intercept) 0.12 0.01 0.11 0.14 1.79 6 20
sd(beta1_Intercept) 0.03 0.00 0.03 0.04 2.23 5 20
sd(beta2_Intercept) 0.19 0.10 0.02 0.35 2.43 5 11
sd(kappa_Intercept) 0.60 0.46 0.17 1.45 2.88 5 24
sd(gamma_Intercept) 5.03 3.67 0.01 10.48 3.27 4 18
Population-Level Effects:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
alpha_Intercept 0.83 0.04 0.71 0.86 1.81 6 26
beta1_Intercept 0.13 0.05 0.10 0.24 2.59 5 21
beta2_Intercept -0.25 0.11 -0.43 -0.10 2.12 5 16
kappa_Intercept 3.18 0.52 2.08 3.80 2.04 6 17
gamma_Intercept 1.12 0.49 0.23 1.83 1.56 7 20
Family Specific Parameters:
Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS
sigma 0.25 0.00 0.24 0.25 1.32 10 51
Draws were sampled using sample(hmc). For each parameter, Bulk_ESS
and Tail_ESS are effective sample size measures, and Rhat is the potential
scale reduction factor on split chains (at convergence, Rhat = 1).